The Heisenberg uncertainty relation in harmonic analysis on p -adic numbers field

Cui Minggen[1]; Zhang Yanying[2]

  • [1] Harbin Institute of Technology Department of Mathematics No.2 WenHua west road WeiHai, ShanDong, 264209 CHINA
  • [2] Harbin Normal University Department of Information Science HeXing Road Harbin,HeiLongJiang, 150080 CHINA

Annales mathématiques Blaise Pascal (2005)

  • Volume: 12, Issue: 1, page 181-193
  • ISSN: 1259-1734

Abstract

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In this paper, two important geometric concepts–grapical center and width, are introduced in p -adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in p -adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on p -adic numbers field.

How to cite

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Minggen, Cui, and Yanying, Zhang. "The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field." Annales mathématiques Blaise Pascal 12.1 (2005): 181-193. <http://eudml.org/doc/10510>.

@article{Minggen2005,
abstract = {In this paper, two important geometric concepts–grapical center and width, are introduced in $p$-adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in $p$-adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on $p$-adic numbers field.},
affiliation = {Harbin Institute of Technology Department of Mathematics No.2 WenHua west road WeiHai, ShanDong, 264209 CHINA; Harbin Normal University Department of Information Science HeXing Road Harbin,HeiLongJiang, 150080 CHINA},
author = {Minggen, Cui, Yanying, Zhang},
journal = {Annales mathématiques Blaise Pascal},
language = {eng},
month = {1},
number = {1},
pages = {181-193},
publisher = {Annales mathématiques Blaise Pascal},
title = {The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field},
url = {http://eudml.org/doc/10510},
volume = {12},
year = {2005},
}

TY - JOUR
AU - Minggen, Cui
AU - Yanying, Zhang
TI - The Heisenberg uncertainty relation in harmonic analysis on $p$-adic numbers field
JO - Annales mathématiques Blaise Pascal
DA - 2005/1//
PB - Annales mathématiques Blaise Pascal
VL - 12
IS - 1
SP - 181
EP - 193
AB - In this paper, two important geometric concepts–grapical center and width, are introduced in $p$-adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in $p$-adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on $p$-adic numbers field.
LA - eng
UR - http://eudml.org/doc/10510
ER -

References

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  1. M. G. Cui, H.M Yao, H.P Liu, The Affine Frame In p -adic Analysis, Annales Mathematiques Blaise Pascal 10 (2003), 297-303 Zbl1066.42501MR2031273
  2. M. G. Cui, On the Wavelet Transform in the field ℚ p of p-adic numbers, Appl. Comput. Harmonic Analysis 13 (2002), 162-168 Zbl1022.42025MR1942750
  3. G.H Gao, M.G Cui, Calculus on the field ℚ p of p -adic numbers, J. of Natural Science of Heilongjiang University 3 (2003), 15-16 
  4. Paul R. Halmos, Measure Theory, (1965), Beijing Scientific Publishing House(Chinese Translation), Beijing 
  5. S. V. Kozyrev, Wavelet theory as p -adic apectral analysis, Izv. Russ, Akad. Nauk, Ser. Math. 66 (2002), 149-158(Russian) Zbl1016.42025MR1918846
  6. V.S Vladimirov, I.V Volovich, E.I Zelenov, p-adic Analysis and Mathematical Physics, Internat. Math. Res. Notices 13 (2996), 6613-663 Zbl0812.46076

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